Close to Reykjavík you can find two airports which might be a bit confusing: The Reykjavíkurflugvöllur (RKV) is very close to the city center and flights inside the country (as well es to Greenland and the Faroes) are operated from there. For most international flights the Keflavíkurflugvöllur (KEF) 50 kilometers afar is used. It is the most important airport of the country and it is the starting point for tourists and travelers on the island.
The Keflavíkurflugvöllur has just one terminal and two runways. 1,8 million passengers are using this airport on the Reykjanes peninsula every year and it was opened in 1943. KEF is a small and very good airport with short ways to walk. An airport bus can take you to the city center but when you like outside the terminal building you immediately see the predominant means of transportation: most people get their rental cars directly at the airport. When you are already thinking about the car return: there are numerous gas stations in villages close to the airport.